[/
  Copyright 2011 - 2020 John Maddock.
  Copyright 2013 - 2019 Paul A. Bristow.
  Copyright 2013 Christopher Kormanyos.

  Distributed under the Boost Software License, Version 1.0.
  (See accompanying file LICENSE_1_0.txt or copy at
  http://www.boost.org/LICENSE_1_0.txt).
]

[section:cpp_rational cpp_rational]

`#include <nil/crypto3/multiprecision/cpp_int.hpp>`

   namespace boost{ namespace multiprecision{

   typedef rational_adaptor<cpp_int_backend<> >    cpp_rational_backend;

   typedef number<cpp_rational_backend>         cpp_rational;

   }} // namespaces

The `cpp_rational_backend` type is used via the typedef `nil::crypto3::multiprecision::cpp_rational`.  It provides
a rational number type that is a drop-in replacement for the native C++ number types, but with unlimited precision.

As well as the usual conversions from arithmetic and string types, instances of `cpp_rational` are copy constructible
and assignable from type `cpp_int`.

There is also a two argument constructor that accepts a numerator and denominator: both of type `cpp_int`.

There are also non-member functions:

   cpp_int numerator(const cpp_rational&);
   cpp_int denominator(const cpp_rational&);

which return the numerator and denominator of the number.

Things you should know when using this type:

* Default constructed `cpp_rational`s have the value zero.
* Division by zero results in a `std::overflow_error` being thrown.
* Conversion from a string results in a `std::runtime_error` being thrown if the string can not be
interpreted as a valid rational number.

[h5 Example:]

[cpp_rational_eg]

[endsect] [/section:rational Rational Number Types]
